Space of modular forms of level 126, weight 3, and Character 126.q

• Label: 126.3.q
• Level: $126$
• Weight: $3$
• Character orbit: 126.q
• Rep. character: $\chi_{126}(29,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

	Total	New	Old
Modular forms	104	24	80
Cusp forms	88	24	64
Eisenstein series	16	0	16

Trace form

24 * q + 24 * q^4 + 36 * q^5 + 8 * q^6 - 32 * q^9 - 24 * q^12 - 44 * q^15 - 48 * q^16 + 48 * q^18 + 24 * q^19 + 72 * q^20 + 28 * q^21 + 24 * q^22 - 72 * q^23 - 16 * q^24 + 72 * q^25 - 108 * q^29 - 56 * q^30 - 60 * q^31 + 104 * q^33 - 48 * q^34 - 80 * q^36 - 168 * q^37 + 144 * q^38 + 64 * q^39 + 108 * q^41 + 60 * q^43 + 116 * q^45 - 324 * q^47 - 48 * q^48 - 84 * q^49 + 144 * q^50 - 268 * q^51 - 208 * q^54 + 264 * q^55 + 60 * q^57 - 432 * q^59 - 32 * q^60 - 192 * q^64 - 180 * q^65 - 112 * q^66 + 72 * q^67 + 72 * q^68 + 536 * q^69 + 96 * q^72 + 24 * q^73 + 288 * q^74 + 76 * q^75 + 24 * q^76 - 64 * q^78 + 12 * q^79 + 544 * q^81 - 288 * q^82 + 756 * q^83 + 112 * q^84 - 156 * q^85 + 360 * q^86 + 280 * q^87 - 48 * q^88 + 80 * q^90 - 168 * q^91 - 144 * q^92 + 436 * q^93 - 936 * q^95 - 64 * q^96 + 48 * q^97 - 440 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
126.3.q.a	$126$	$3$	126.q	9.d	$6$	$24$	$12$	$3.433$		None		✓	✓	✓	126.3.q.a	$2$	$0$	\(0\)	\(0\)	\(36\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)